Math does matter

Juxtaposition fans, rejoice. The Washington Post has done it again! In an opinion piece titled, “How much math do we really need?” (10/23/2010) G. V. Ramanathan, professor emeritus of mathematics, statistics and related subjects at the University of Illinois, Chicago argues, “Unlike literature, history, politics and music, math has little relevance to everyday life.” It […]

According to the editorial, “A 2008 study by economists Mihir Desai, C. Fritz Foley, and James Hines of Harvard Business School found that domestic investment by U.S. firms grows by 2.6 percent for each 10 percent increment in the companies’ investment overseas.” It cited this as evidence of the economic benefits of sending work offshore.

Had the editorial team been more adept at mathematical reasoning, it might have compared this 2.6 percent benefit to the growth of domestic investment by U.S. firms when they invest the same 10 percent increment domestically instead of in foreign subsidiaries.

Which would be … let’s see … carry the one … that would be … hmmm … 10 percent — nearly four times bigger.

And why percentages? If a company has $1 billion in U.S. assets and a hundred bucks worth in Malaysia, then investing another ten bucks in Kuala Lumpur should yield $26 million here.

Sign me up!

The most important reason to learn more math (and science; the two go hand in hand) is, clearly, self-defense.

The paper’s authors were, thankfully, more cautious in their assessment than the Post. They limited their conclusion to recognizing that investments in foreign subsidiaries correlate with increases in a firm’s domestic activity, rather than the decreases many expect.

They were silent on the comparison between the impacts of investing in foreign and domestic subsidiaries, and said nothing at all about outsourcing.

When an organization as respected as the Washington Post commits reasoning this specious, it’s a warning to us all.

Bad logic is a non-partisan crime. Here’s how more knowledge of science and math might have kept the Post out of trouble:

Scientists know to understand the hypothesis being tested. In this case, it was U.S. companies that invest in foreign subsidiaries invest more domestically than companies that don’t invest anywhere. They’d spot the difference between it and other, related hypotheses such as, the U.S. is better off when a company invests abroad than when it invests domestically — what the editorial claimed was demonstrated.

The editorial’s phrasing also strongly implied a causal relationship. Scientists are more careful. In the cited paper, the researchers were clear that correlation was the best they could manage.

Which isn’t surprising. Anyone familiar with how accounting systems work know they don’t demonstrate cause-and-effect relationships, and in fact very few businesses have any tools for reliably demonstrating the connection between corporate action and bottom-line results (for more on this see “Measure? If you can’t predict you can’t manage,” KJR, 8/16/2010).

Also: The paper’s raw data consisted of individual business results, which were then aggregated for analysis. The results show how those businesses that invested in foreign subsidiaries fared domestically, not how the U.S. economy fared as a result of those investments.

(Here’s why they might be different: Having foreign subsidiaries implies a certain minimum size on the part of the investing companies. Their increased domestic success was probably at the expense of U.S. firms too small to open foreign branches. This consequence could easily cancel out at least some, possibly all, and imaginably more than the cited benefits.)

So here’s what we know: On average, U.S. firms that increase investment in foreign subsidiaries also increase domestic investment.

Here’s what we don’t know: Whether these two increases are connected; how much actual money is involved; whether the firms would have done better or worse had they invested domestically instead; the net onshore impact of offshore outsourcing; and whether the U.S. economy is better or worse off because of the increased foreign investment.

In case you think I’m advocating policy changes, tax changes, or stern looks of disapproval directed toward companies that send work overseas, or you think I’m defending the Democratic Party from an attack by the Post …

Naw. This is meant as a cautionary tale, “Ripped from today’s headlines!”

The point? You deal with parallels every day, in the form of internal analyses and reports from various research firms.

Bravo! This is a dying horse I’ve been beating for years (even before I had a high-schooler complaining about how she’ll never use the math and science she’s so unfairly being forced to learn…) Sound logical understanding and statistical analysis prove their utility every day. In just the past 48 hours I’ve used them dozens of times, in all sorts of settings:

– I quashed a $50,000 solution management was embracing by demonstrating that it was a fix for a $500 problem.

– I identified a small and painless process change that eliminated the same $500 issue at no cost.

– I deciphered the byzantine changes to my employee benefits election process that ensued following the recent changes in Health Insurance law. Without some rigourous and detailed analysis it would have been easy to overpay or leave my family under-covered.

– I unraveled the “actual” (as opposed to the “advertised”) impacts of several ballot measures proposing seemingly minor esoteric tweeks to various state laws, and cast votes consistent with my own fiscal and ethical values.

– I helped the aforementioned high-schooler with her math (statistics and probability) and science (scientific method theory and physics) homework (she hates it when I actually seem excited about this…)

– I cleaned up at my weekly card game and continuted dominating all of the jocks in my fantasy football league.

It actually scares the bejeezus out of me that that such a large percentage of the population (including people like the Washington Post reporters and Emeritus Statistics professors) is perfectly comfortable with their own individual and collective illiteracy when it comes to math and science. It makes me wonder how many of our business issues, personal problems, and public policy ills could be avoided altogether if more decision making was based on rational analysis rather than “intuition”, “conventional wisdom”, fear, anger, personal prejudice, and the like.

Perhaps my least favorite flavor of this illiteracy is “illion-itis” – the inability of most people to fathom the geometric differences between thousands, millions, billions, trillions, and so forth. This is especially troublesome in public policy debates, where the failure of may citizens to distiguish between massive orders of magnitude make it easy to inflame people over minor points even as they ignore major crisises.

Unfortunately, it seems like the ingnorance is increasingly willfull: Any attempt to shed some reasonable light on one of these subjects, even in the simplest mathematical terms, often invites a serious anti-intellectual backlash. People accuse you of “getting all mathy” on them.

As it becomes impossible to turn on the TV or Radio during election seasons without being subjected to an endless streams of deliberate misinformation, it seems clear that lots of mathematically and scientifically savvy people on all sides have done the reasearch, analyzed the data, and concluded that (Mr. Lincoln notwithstanding) it is increasingly possible to fool a lot of the people a lot of the time. Sure you can get along without math and science, provided you don’t mind being perpetually at the mercy of those who want to use them against you.

In (hypothetical) defense of G. V. Ramanathan, professor emeritus, he may have needed to finish his thought by saying something like “but they really need to understand arithmetic, counting, calculation, measurement and similar tools.”

Some of the stuff of mathematics makes your head hurt. But if you are unable to figure out where to put your money, how much paint you need to do the living room or the bandwidth you need for your server, you are in a world of hurt.

What I have found over the years, in companies both large and small, is that managers do not like it when you apply logic and reasoning that is contrary to their proposed direction. Rather than consider that an alternate viewpoint might be more valid than their own, you are instead considered a troublemaker. They resort to name calling: “Why can’t you get with the program?”, “Why can’t you see my vision, my mission, my strategy?”. They’ve developed a strategy, even tactics that they think will achieve it, without ever considering that there could be other more optimal tactics to achieve their goal. They never even consider that their strategy might be flawed.

Psychologists refer to this as cognitive dissonance: a disregard for facts that are contrary to your personal beliefs.

Science, mathematics, reasoning, logic, critical thinking: these are all fine qualities for anyone to possess. The “theory, test, validate, adapt, or reject” nature of science is the best way we have ever found to improve human conditions. Unfortunately, those in a position of power only look at primary effects: if I do this, that will happen. They rarely consider secondary effects let alone tertiary or quaternary side effects. Too bad they didn’t have a background in mathematics to instill in them the discipline to logically think things through.

I agree completely with this week’s KJR column (10/25/2010: Math does matter) and I think the problem goes beyond math. Decision-making is mostly math since logic is a branch of math. However, the major flaw in many cases of faulty logic is incomplete information based on a lack of critical inquisition and examination. These flaws are usually due to laziness or inadequate training. Also, as a society we have grown too enamored with binary, all-or-nothing decisions. Yet the world rarely works in just two ways…

A significant flaw in the study cited is the assumption that all products/services and markets behave the same way in the global economy. They probably follow similar rules but their behavior varies based on factors that were not identified. To name a few…

> What is the nature of demand (consumer, industrial, infrastructure, etc.)?
> Is the product/service simple or complex?
> Are other providers/sources (competitors) plentiful or few?
– Where are they?
– Does location of operations provide a competitive advantage for anyone?
> Is demand localized or universal?
> Resource availability to establish operations (talent, capital, raw materials, etc.).

Interestingly, the company I work for has experienced greater demand for US-made products after establishing a manufacturing facility (for other products) in a foreign country. In those cases, foreign investment had a direct positive impact on sales of US-made products. This has been repeated many times and its validity is solid. But I believe this phenomenon is unique to the particular industry in which we compete (based on some of the factors listed above). It also helps that our management understands this phenomenon and considers its impact when executing our business plan.

The original author did leave themselves a fairly large cop-out clause — “All the mathematics one needs in real life can be learned in early years…” (presumably +,-,*,/) Which would be helpful, except that the WP article then wrongly applied “early years” math as Bob pointed out.

And of the professions the author singles out — plumber, lawyer, grocer, mechanic, physician — it takes like 3 seconds to come up with math use-cases for each one.

Granted, the plumber installing your tub may not be well-versed in differential equations as they relate to pressure calculations — but someone in the plumbing profession had better know it!

And physicians don’t use math?? Wow. Not sure where to even start with that one.

Mathematics professors don’t use the term “math” as normal people do. Ramanathan is right: modern pure mathematics has little relevance to everyday life.

With the death of Benoît Mandelbrot fresh on my mind, I find myself hard put to find practical everyday relevance for the dimensionality of the Koch curve.

Bob, your mathematical reasoning example merely requires elementary school arithmetic. If Professor Ramanathan had claimed that arithmetic has little relevance to everyday life, he would have been wrong. But that’s not what he said, nor what he meant.

As I see it, we could do worlds of good by getting people to mentally compartmentalize different areas of mathematics. As a first step, I’d say we should stop using the term entirely for what is taught in elementary school. Small children are not learning math, they’re learning arithmetic. I think if we could get people to gain confidence that they can truly master arithmetic and stop being concerned that the full magisterium of mathematics is beyond them, we’d see a lot more people applying that limited but oh-so-useful mastery more often.

Let the hoi polloi continue to fear pure mathematics; ’tis truly fearsome. What we should be concerned about is the “math is hard” problem.

I am a DIY electronics hobbyist, and I see this problem in that world, surprisingly enough. Electrical engineering is applied physics, so there’s frequent need to use math, but in the DIY world, there are a lot of dilettantes who will shy away even from simple things like Ohm’s Law: fractions, division, multipication…arithmetic. It is truly dismaying.

The only other branch of mathematics that would be good for the general public to master is elementary statistics. But here, I think we’re entirely missing some term of distinction. What statisticians mean by the term “statistics” is almost an entirely different subject from what is useful in everyday life. I want Joe Voter to be able to make meaningful comparisons of reported poll exit data; I don’t care that Joe Voter cannot load the raw data up into R and run an ANOVA test on it.

Bear in mind that the Post editorial comes as much from the paper’s point of view as from any degree of innumeracy. The editorial writer could easily have understood everything said here, but if it didn’t agree with his or her preconceived notions, or the Post’s editorial biases, then mathematical logic and sense were dispensable.

As usual, I largely agree with Bob Lewis. I am jumping in here to try to boost a notion of my own that is provoked by ‘In an opinion piece titled, “How much math do we really need?” (10/23/2010) G. V. Ramanathan, professor emeritus of mathematics, statistics and related subjects at the University of Illinois, Chicago argues, “Unlike literature, history, politics and music, math has little relevance to everyday life.”
It appears Ramanathan knows math better than self-reinforcing feedback loops: Math has little relevance to those who have decided it has little relevance.’
In the days since I was a full-time mathematics teacher, I am increasing convinced that mathematics is simply consciously accurate communication (and that consciously accurate communication is mathematics). Of course, what passes for mathematics and its instruction in our country offers many counterexamples to this. If what Professor Ramanathan has professed for all these years is not primarily concerned with accurately sharing thoughts, that is a great sadness. Literature, history, politics, music, not to mention marketing, entertainment, economics hardly ever try to play “let’s you and I have exactly the same thought.”
We do not think our children will be daily faced with considering the situation “Two trains leave their stations at 8:00am, one headed for Pittsburgh from Philadelphia and the other headed for Philadelphia from Pittsburgh…” What we do want is that they will have attention spans long enough, and a knowledge base stocked well enough, and enough persistence to put their on pieces together to be able to say “Yes, I know that such trains will meet at this time, at this distance from Philly.”
What do you think?

Bob Lewis is a senior management consultant with Dell Services. He has published these columns once a week in one form or another since 1996.

Disclaimer: All opinions, statements, representations, allegations, images (if published) and anything else that appears here is the sole responsibility of the author. Dell has and had nothing to do with it, other than saying it's okay to continue publishing KJR.